NEW YORK, May 1 (Reuters) - The S&P 500 edged higher on Tuesday after comments from a Trump administration official on trade with China and the Mexican economy minister on the renegotiation of the North American Free Trade Agreement provided cause for optimism.

Mexican Economy Minister Ildefonso Guajardo said his country would respond to U.S. proposals on rules for automobiles under NAFTA next week and that a deal is likely if negotiators show enough creativity and flexibility.

Earlier, stocks came off the day's lows after U.S. Trade Representative Robert Lighthizer said he did not desire to change China's economic system but wanted to limit the damage it causes to the United States and encourage more foreign competition.

The encouraging news on trade balanced concerns of inflation, which sent stocks lower at the start of the session.

"There is a certain level of fear that has seeped into this market," said Tim Ghriskey, chief investment strategist at Inverness Counsel in New York. "But there are positive outlooks out there on trade."

The Dow Jones Industrial Average fell 64.1 points, or 0.27 percent, to 24,099.05, the S&P 500 gained 6.75 points, or 0.25 percent, to 2,654.8 and the Nasdaq Composite added 64.44 points, or 0.91 percent, to 7,130.70.

Despite Tuesday's slight gains, investors say they remain concerned about cost warnings from companies, even as the current earnings season, now past the halfway mark, has produced the strongest profit growth in seven years.

Data from the Institute for Supply Management indicated a jump in raw material costs for U.S. companies, in part due to the tariffs on steel and aluminum imports imposed by the Trump administration. It also showed that U.S. factory activity slowed for a second straight month in April.

Oil prices are near their highest levels since 2014, though they dropped more than 1 percent on Tuesday as the dollar remained near a four-month high.

"The red flags are everywhere," said Jim Awad, senior managing director of Hartland & Co in New York. "We're finally getting the inflation that to date has been so elusive."

Rising costs have stoked fears that the Federal Reserve will raise interest rates more times than expected this year. The U.S. central bank's Federal Open Market Committee is scheduled to release its policy statement on Wednesday at the close of a two-day meeting. It is expected to keep interest rates steady but will likely encourage expectations that it will hike rates in June.

Shares of Pfizer Inc fell 3.3 percent, the greatest percentage decline on the Dow, after the company posted its biggest miss on quarterly revenue in a year as demand for key drugs fell short of estimates.

Apple Inc shares rose more than 4 percent after the bell following the company's quarterly results.

Shares of Match Group Inc, the owner of dating app Tinder, and IAC/InterActiveCorp, Match's parent company, dropped after Facebook Inc announced that it would add dating features to its flagship social network. Match shares tumbled 22.1 percent while IAC shares sank 17.8 percent. Facebook shares rose 1.1 percent.

Advancing issues outnumbered declining ones on the NYSE by a 1.10-to-1 ratio; on Nasdaq, a 1.43-to-1 ratio favored advancers.

The S&P 500 posted four new 52-week highs and 29 new lows; the Nasdaq Composite recorded 36 new highs and 72 new lows.

Volume on U.S. exchanges was 6.56 billion shares, compared to the 6.54 billion average for the full session over the last 20 trading days. (Additional reporting by Sruthi Shankar and Savio D'Souza in Bengaluru; Editing by Jonathan Oatis and Leslie Adler)